Proposition 4.8 (Corollary 9.5 in [1]}) 
For any \(i\ne j\) , we have
\(\bigoplus _{m+n=1-(i,j)\atop \textrm { m is odd}}L_{mi}\ast L_{j}\ast L_{ni}\simeq \bigoplus _{m+n=1-(i,j)\atop \textrm { m is even}}L_{mi}\ast L_{j}\ast L_{ni}.\) 

